Question

已知tan(x+y)=3,tan(x-y)=1/2,则sin2x/sin2y=

Answer 1

tan(x+y)+tan(x-y)=sin(2x)/(cosxcosy)=3+1/2=7/2

tan(x+y)-tan(x-y)=sin(2y)/(cosxcosy)=3-1/2=5/2

sin(2x)/sin(2y)=[tan(x+y)+tan(x-y)]/[tan(x+y)-tan(x-y)]=7/2/(5/2)=7/5